Algebra

Simplify: $4x + 7 - 2x + 1$.

Find the value of $3n - 1$ when $n = 0$.

Expand: $2(3a + 4b)$.

Solve for $t$: $\frac{20}{t} = 5$.

Factorize the expression: $x^2y + xy^2$.

If three times a number $n$ added to 10 results in 31, what is the value of $n$?

Simplify the expression: $3x^2y + 4xy^2 - 2x^2y$.

Solve for $x$: $3(x+4) = 2(x-1) + 10$.

If $a = -1$, evaluate $3a^3 - 2a^2 + 5a - 1$.

Solve the equation: $\frac{1}{2}(4x - 8) = \frac{2}{3}(6x - 9)$.

Determine the next term in this linear sequence: $-50, -40, -30, -20, \dots$

If the term-to-term rule is 'add $12$' and the first term is $8$, what is the $2^{nd}$ term?

What is the common difference for the sequence: $10, 7, 4, 1, \dots$?

Find the $10^{th}$ term of the sequence: $7, 14, 21, 28, \dots$

Calculate the $n^{th}$ term for the sequence $10, 6, 2, -2, \dots$

If $U_n = 8n + 3$, which term number is equal to $163$?

Find the $n^{th}$ term of the sequence $20, 15, 10, 5, \dots$

Which term in the sequence $U_n = 10 - 2n$ is equal to $-50$?

A sequence is $U_n = 4n - 1$. Calculate $U_{10} - U_5$.

Find the $20^{th}$ term of the sequence $x-4, x, x+4, \dots$.

A mapping machine follows the rule: 'Multiply the input $x$ by 3, then subtract 2 to find the output $y$'. Which of the following equations represents this function?

Which of the following points lies on the line shown in the diagram, which represents the function $y = x + 2$?

The diagram shows a function machine. If the input is $x$, the machine multiplies the input by 3 and then subtracts 5. What is the output when the input is $7$?

What is the output of the function $y = 10 - x$ when $x = 4$?

The diagram shows the graph of the linear function $y = x + 3$. At what coordinates does the line cross the x-axis?

The graph shows a linear relationship between $x$ and $y$. Based on the points provided on the graph, identify the correct function rule.

The diagram shows two function machines. Machine 1 takes an input and adds 4. Machine 2 takes the result and multiplies by 2. If the final output is $18$, what was the original input $x$?

A rental company charges $20$ to rent a bicycle plus $5$ per hour. A second company charges $10$ to rent a bicycle plus $7$ per hour. After how many hours $x$ is the cost $y$ the same for both companies?

Consider the mapping diagram shown. If the relationship is a linear function of the form $y = ax + b$, find the value of $y$ when $x = 10$.

A submarine is at a depth of $500$ meters below sea level and starts ascending at a rate of $25$ meters per minute. If $y$ represents the depth (where sea level is $0$ and depths are negative), which function describes the submarine's depth after $x$ minutes, and when will it reach a depth of $-150$ meters?

Simplify the following expression: $15x - 10x + x$.

Simplify: $z + z + z + z$.

Expand the bracket: $3(h + 5)$.

Simplify: $2 \times 9c$.

Simplify: $3a - [2a - (a + 1)]$.

Simplify: $4(x^2 + 2x) - 2(2x^2 - x)$.

Simplify: $(x + 2) + (x + 3) - (x - 4)$.

Simplify: $\frac{x+1}{2} + \frac{x+2}{3} + \frac{x+3}{6}$.

Simplify the expression: $a - [a - (a - (a - b))]$.

Simplify: $0.25(8x - 12y) - 0.5(4x + 6y)$.